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I like to digest better:

  • the $* d * $ operator in Maxwell differential form equation

  • the $* D * $ operator in Yang-Mills differential form equation

We already knew that in Maxwell differential form equation we have: $$ * d * F=0 $$ knew that in Yang-Mills differential form equation we have: $$ * D * F=0 $$ here $D .=d .+ [A,.]$

But how we do understand $* d * $ operator and $* D * $ operator? Their the (differential/geometry) meaning? How do we make ourselves comfortable , even though we also knew the equation boils down to:

$$ \partial_\mu F^{\mu \nu}=0 $$ $$ D_\mu F^{\mu \nu}=0 $$ respectively. But how to think $* d * $ operator and $* D * $ operator differential/geometry-ly?

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  • $\begingroup$ Well, do you understand what $\ast$ and $d$ individually mean? $\endgroup$ – d_b May 20 at 21:46

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